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R-L circuit/inductance problem

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

    An RL circuit has a 60V battery, a 42H inductor, a 24Ω resistor and a switch, all in series. Initially the switch is open and there is no magnetic flux in the inductor. At t=0 the switch is closed. When the inductor voltage is 24 V, the time t is closest to?


    2. Relevant equations

    i(t) = I(1-e-t/[itex]\tau[/itex])

    [itex]\epsilon[/itex]=IR

    3. The attempt at a solution

    i'm confused by this problem for some reason but what i tried to do was set 60/24 to solve for initial current but i guess if this is a growth problem so i'm not sure what else to do...the answer i got was t=0.9s but i know thats not right
     
  2. jcsd
  3. Apr 28, 2012 #2

    NascentOxygen

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    Staff: Mentor

    Hi bdh2991! Your equation i(t) = I(1-e-t/τ ) is spot on!

    ⚑ What do you calculate to be the value of τ in this circuit? (Incidently, for τ what would be its units?)

    ⚑ When the voltage across the inductor is 24V, how many volts would there be across the resistor?

    ⚑ In your equation for i(t), how will you determine what value to use for I?
     
  4. Apr 28, 2012 #3
    [itex]\tau[/itex]would = L/R but i believe its units are seconds, numerically it would be 1.75s

    I was thinking the voltage across the resistor would be 60= V + 24, so 36V

    and the value for I is what i'm confused about, I thought that I is the initial current so it would just be [itex]\epsilon[/itex] = IR, 60=I(24), so I = 2.5?
     
  5. Apr 28, 2012 #4

    NascentOxygen

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    Looking at the equation for i(t), what value of time t would get rid of the exponential term, i.e., make the exponential term = 0?
     
  6. Apr 28, 2012 #5
    at t=0 the exponential would be e^(0) which would equal 1 so i(t) = I (0) = 0
     
  7. Apr 28, 2012 #6

    NascentOxygen

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    Correct. The current starts from a very low value. But the question I asked was:
     
  8. Apr 28, 2012 #7
    I got 0.83 seconds, but I didn't check it properly.
     
  9. Apr 28, 2012 #8
    i thought and e function could never = 0 ?

    why do i feel like i should have gotten what your trying to tell me already
     
  10. Apr 28, 2012 #9

    NascentOxygen

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    Well, it approaches zero. I'm angling for either 0, τ, or ∞. Which one? :wink:

    And when e-t/τ =0, what does your i(t) equation reduce to?
     
  11. Apr 28, 2012 #10
    I'm interested to know now too, I get 1.922s now and I am supposed to remember this stuff!
     
  12. Apr 28, 2012 #11
    i see when t approaches infinity then the equation reduces to i(t) = I, or i guess stabalizes
     
  13. Apr 28, 2012 #12
    So what would be the current at t = infinity?
     
  14. Apr 28, 2012 #13
    I = 24/24 so I = 1?
     
  15. Apr 28, 2012 #14
    No. What would the circuit look like at t = infinity? I.e. what is the inductor acting like at t = infinity? (Property of an inductor)
     
  16. Apr 28, 2012 #15

    NascentOxygen

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    Yes, most DC circuits given enough time do reach a steady current and voltage. :smile:

    Doing well. :smile:

    From your knowledge of DC and inductors in circuits, you know that the voltage across an inductor is di/dt. But when circuit currents and voltages have all settled down to steady values, di/dt = 0 so the voltage across every inductor is 0.

    As you can see, I is the final current, the current after infinite time has elapsed.

    At t=∞, with the voltage across the inductor equal to zero, all the voltage appears across the resistor. So you can calculate for your circuit's voltage and resistor values that final circuit current, I has a value = https://www.physicsforums.com/images/icons/icon5.gif [Broken]
     
    Last edited by a moderator: May 5, 2017
  17. Apr 28, 2012 #16
    ok so the if the voltage across the conductor is 0 then 60= v +0, therefore v = 60 and R stays the same 24 ohms so I = 2.5 A?
     
  18. Apr 28, 2012 #17

    NascentOxygen

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    conductor? You mean inductor?

    Yes, I=2.5A.

    Knowing values for I and τ, you have found the equation exactly describing i(t) from t=0 through to t=∞.

    That's all you need to be able to finish the question. The remainder is just mathematical manipulation. Are you okay with it now?
     
  19. Apr 28, 2012 #18
    Yes i think i got it now but just to make certain

    To get the actual answer it would be 1=2.5(1-e-t/1.75) then just solve for t
     
  20. Apr 28, 2012 #19

    NascentOxygen

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    You haven't explained where that 1 on the LHS magically appeared from. :confused:

    The equation is i(t) = 2.5(1 – e-t/1.75) where i(t) is the current through each of L and R. You are asked to determine t when a particular voltage = 24V. You haven't shown an equation relating voltage to time for any element, yet, so you need to come up with one. Write it out explicitly. (Hint: it's easy. :wink:)

    And there was a further hint back when I asked:

    See how you go now. Don't forget, there is always more than one way to solve a circuit problem. If you can see two ways, then you have a means for checking your first solution. :shy:
     
  21. Apr 28, 2012 #20
    i got 1 from taking the voltage across the inductor which would be 24v and divided it by the resistance 24 ohms then substituting it in for the current. if you were to use the voltage of the resister, 36v, then divide by the resistance of 24 ohms you would get i = 2.5 A for that instant but why would you use the voltage across the resistor to solve for the current across the inductor????????

    i'll never understand physics lol
     
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